
Sketches are considered to be a collection of 5-tuple \((\Delta x, \Delta y, q_1, q_2, q_3)\) , where \((\Delta x, \Delta y)\)  are the offsets to be moved along \(X\)  and \(Y\)  axes respectively and \((q_1, q_2, q_3)\)  is the pen-state. \((q_1, q_2, q_3)=(1,0,0)\)  indicates that the pen is on the paper, \((q_1, q_2, q_3)=(0,1,0)\)  indicates it is lifted and \((q_1, q_2, q_3)=(0,0,1)\)  indicates that the drawing has ended. Pen-state is modeled as categorical random variable. All the drawings are assumed to start from the origin. This is done by prepending the sketch with the start-of-sequence symbol \(S_0\) , which is \((0,0,1,0,0)\) . The offsets are modeled as a Gaussian Mixture Model (GMM) in the case of SkeGAN and as IID normal variable in the case of VASkeGAN. In both the models, we incorporate the parameter \(\tau \in [0,1]\)  as defined in [1]}, to control the randomness or the variety in the generated samples. Sketch generation is done tuple-by-tuple until \(q_3\)  is not 1 or until the maximum length \(N_{max}\)  is reached. A sketch is generated stroke by stroke, wherein the stroke at time-step \(i\)  depends on all of the strokes at previous time-steps. In order to model this dependency, the generator is an auto-regressive model like LSTM or GRU. The discriminator distinguishes whether a batch of sketches has come from the dataset or from the generator. So it must understand the dependency between strokes of different time-steps in order to distinguish the sketches. Therefore, the discriminator is also an auto-regressive model like LSTM or GRU.
